Embed Size (px)
Citation preview
Class 4Fractions
For more such worksheets visit www.edugain.com
Answer the questions
(1) Solve : 1
22 +
2
22 +
3
22
(2) Shade the images to show the following fraction subtraction.
9
10 −
4
10 =
− =
(3) What is the value of ?
4
17 +
17 +
1
17 +
6
17 = 1
(4) George read 7
8 of a book in two days. If George read
4
8 of the book on the first day. What fraction
of the book he read on the second day?
(5) The following figure shows different fruits in a basket. What fraction of the fruits are pomegranates?
(6) The perimeter of a square board is 5
7 m. Find the length of each side in meters.
(7) What fraction is represented by shaded portion of these shapes :
ID : in-4-Fractions [1]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
A)
B)
C)
D)
E)
F)
(8) What will be the numerator of the fraction representing the unshaded part in the given figure ?
(9) Tina's school is 6
7 kilometers away. She normally picks up her friend on her way to school. If the
distance of her friend's house is 5
7 kilometers from her house. Find the distance of the school from
her friend's house?
(10) Write the mixed fraction representred by the figure given below.
ID : in-4-Fractions [2]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Choose correct answer(s) from the given choices
(11) The figure representing the fraction of the shaded part equivalent to 8
14 is ______.
a. b.
c. d.
Fill in the blanks
(12) Add the following fractions:
A) 3
10 +
5
10 =
B) 3
12 +
8
12 =
C) 1
3 +
1
3 =
D) 7
17 +
7
17 =
E) 3
15 +
8
15 =
F) 5
16 +
6
16 =
(13) Add the following fractions and reduce them to the simplest form:
A) 5
4 +
8
2 = B)
5
9 +
4
5 = C)
3
8 +
7
2 =
D) 4
5 +
7
10 = E)
1
5 +
8
7 = F)
5
3 +
6
2 =
(14) A fraction in which the denominator is smaller than the numerator is called an
fraction.
(15) In like fractions, the numerator, the smaller the fraction will be.
ID : in-4-Fractions [3]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
© 2017 Edugain (www.edugain.com). All Rights Reserved
Many more such worksheets can begenerated at www.edugain.com
ID : in-4-Fractions [4]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Answers
(1) 6
22
Step 1
1
22 ,
2
22 and
3
22 are ‘Like Fractions’ - that is, their denominators are the same.
Step 2
In order to add three Like Fractions, we need to add the numerators together and the denominatorremains the same.
Step 3
So, 1
22 +
2
22 +
3
22 =
6
22
ID : in-4-Fractions [5]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(2) 9
10 −
4
10 =
5
10
− =
Step 1
A proper fraction represents a part of a whole. In the given figures, each circle represents onewhole thing, and has been divided into 10 equal parts.
Step 2
The fact that only 9 parts are shaded in the first circle tells us that it represents the fraction 9
10
or ‘9 parts of a thing that has been broken into 10 parts’.
Step 3
Similarly, the second circle represents ‘4 parts of a thing that has been broken into 10 parts’.
Step 4
9 parts minus 4 parts of something that has been broken into 10 parts will be same as ‘5 parts out
of 10’, or 5
10 .
Step 5
So, our answer is 5
10 and this can be represented using the third circle by shading 5 parts out of
10.
ID : in-4-Fractions [6]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(3) 6
Step 1
It is given that sum of fractions is equal to 1. Therefore, numerator and denominator of the sumshould be equal.
Step 2
On addition of fraction we get:
4
17 +
17 +
1
17 +
6
17 =
4 + + 1 + 6
17
Step 3
As we know that numerator and denominator of sum are equal:4 + + 1 + 6 = 17
Step 4
Now, we can be seen that the above relation is satisfied only when is equal to 6.
Therefore, = 6
(4) 3
8
Step 1
Fraction of the book read by George in two days = 7
8
Fraction of the book read by George on the first day = 4
8
Step 2
Fraction of the book read by George on the second day = Fraction of the book read by George intwo days − Fraction of the book read by George on the first day
= 7
8 −
4
8
= 7 − 4
8
= 3
8
ID : in-4-Fractions [7]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(5) 5
15
Step 1
Let us count all fruits in the given box. There are total 15 fruits, out of which 5 are pomegranates.
Step 2
Therefore, fraction of pomegranates = Number of pomegranates
Total number of fruits
= 5
15
(6) 5
28 m
Step 1
According to the question, the perimeter of the square board is 5
7 m and we have to calculate
the length of each side.
Step 2
We know that the perimeter of a square = 4 × side of the squareSo, to calculate the side of the given square, we have to divide the perimeter by 4.Side of the square = Perimeter of the square ÷ 4
= 5
7 ÷ 4
= 5
7 ×
1
4 =
5
28
Step 3
To convert the fraction into the simplest form, let us divide the numerator and denominator of theabove fraction by their H.C.F, that is 1.
5
28 =
5
1
28
1
= 5
28
Step 4
Hence, the length of each side of the square board is 5
28 m.
ID : in-4-Fractions [8]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(7) A) 9
10
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 10Number of parts that are shaded in the image = 9
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 9
10
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 9
10 .
ID : in-4-Fractions [9]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
B) 7
9
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 9Number of parts that are shaded in the image = 7
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 7
9
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 7
9 .
ID : in-4-Fractions [10]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
C) 5
10
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 10Number of parts that are shaded in the image = 5
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 5
10
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 5
10 .
ID : in-4-Fractions [11]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
D) 4
8
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 8Number of parts that are shaded in the image = 4
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 4
8
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 4
8 .
ID : in-4-Fractions [12]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
E) 2
4
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 4Number of parts that are shaded in the image = 2
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 2
4
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 2
4 .
ID : in-4-Fractions [13]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
F) 7
8
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 8Number of parts that are shaded in the image = 7
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 7
8
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 7
8 .
(8) 5
Step 1
We know that a fraction means a part of the whole where the numerator of the fraction representsthe number of parts we have and the denominator represents the total number of parts the figure isdivided into.
Step 2
In the given figure, 5 out of 13 parts are unshaded.Therefore, the numerator of the fraction representing the unshaded part is 5.
ID : in-4-Fractions [14]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(9) 1
7
Tina picks up her friend on her way to school. This means that her friend's house is located on herway to school.So, Distance between the school and her friend's house = Distance between her house and theschool − Distance between her house and her friend's house
= 6
7 −
5
7
= 6 − 5
7
= 1
7
(10) 55
9
Step 1
A mixed fraction has two parts:
1. A whole number representing few whole/complete entities.2. a proper fraction representing a specific part of a whole entity.
Step 2
Here, we can see that there are 5 figures that are shaded completely. They represent the wholenumber part 5 of the mixed fraction.
Step 3
The last figure has 5 out of 9 parts shaded. This represents the proper fraction part 5
9 of the
mixed fraction.
Step 4
Hence, the mixed-fraction shown by the given figure is 5 + 5
9 , or 5
5
9 .
ID : in-4-Fractions [15]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(11) a.
Step 1
We know,
Fraction of the shaded part = Number of shaded parts
Total number of parts
Step 2
Let us find the fraction of the shaded part for each of the given options.
Option a: Fraction of the shaded part = 8
14
Option b: Fraction of the shaded part = 3
14
Option c: Fraction of the shaded part = 4
10
Option d: Fraction of the shaded part = 1
10
Step 3
We have to find the fraction that is equivalent to 8
14 .
Step 4
We find that 8
14 is the fraction of the shaded part of the figure given in option a. Hence, option a
is the correct answer.
ID : in-4-Fractions [16]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(12) A) 3
10 +
5
10 =
8
10
Step 1
3
10 and
5
10 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
10 +
5
10 =
8
10
B) 3
12 +
8
12 =
11
12
Step 1
3
12 and
8
12 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
12 +
8
12 =
11
12
ID : in-4-Fractions [17]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
C) 1
3 +
1
3 =
2
3
Step 1
1
3 and
1
3 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 1
3 +
1
3 =
2
3
D) 7
17 +
7
17 =
14
17
Step 1
7
17 and
7
17 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 7
17 +
7
17 =
14
17
ID : in-4-Fractions [18]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
E) 3
15 +
8
15 =
11
15
Step 1
3
15 and
8
15 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
15 +
8
15 =
11
15
F) 5
16 +
6
16 =
11
16
Step 1
5
16 and
6
16 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 5
16 +
6
16 =
11
16
(13) A) 5
4 +
8
2 =
21
4
Step 1
The fractions 5
4 and
8
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
ID : in-4-Fractions [19]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Let us first find the LCM of the denominators 2 and 4. The LCM is 4.
Step 3
To write 5
4 as an equivalent fraction which has 4 as denominator, we need to
multiply both the numerator and denominator by 4
4 = 1. So, the equivalent fraction is:
5 × 1
4 × 1 =
5
4
Step 4
Similarly, to write 8
2 as an equivalent fraction which has 4 as denominator, we need
to multiply both the numerator and denominator by 4
2 = 2. So, the equivalent fraction
is:
8 × 2
2 × 2 =
16
4
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
5
4 +
16
4 =
5 + 16
4 =
21
4
Step 6
In order to convert the fraction 21
4 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 21 and 4 is 1.
Step 8
Hence, the simplest/lowest form of 21
4 is
21
1
4
1
= 21
4
B) 5
9 +
4
5 =
61
45
ID : in-4-Fractions [20]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Step 1
The fractions 5
9 and
4
5 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 5 and 9. The LCM is 45.
Step 3
To write 5
9 as an equivalent fraction which has 45 as denominator, we need to
multiply both the numerator and denominator by 45
9 = 5. So, the equivalent fraction
is:
5 × 5
9 × 5 =
25
45
Step 4
Similarly, to write 4
5 as an equivalent fraction which has 45 as denominator, we need
to multiply both the numerator and denominator by 45
5 = 9. So, the equivalent
fraction is:
4 × 9
5 × 9 =
36
45
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
25
45 +
36
45 =
25 + 36
45 =
61
45
Step 6
In order to convert the fraction 61
45 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 61 and 45 is 1.
Step 8
ID : in-4-Fractions [21]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Hence, the simplest/lowest form of 61
45 is
61
1
45
1
= 61
45
C) 3
8 +
7
2 =
31
8
Step 1
The fractions 3
8 and
7
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 2 and 8. The LCM is 8.
Step 3
To write 3
8 as an equivalent fraction which has 8 as denominator, we need to
multiply both the numerator and denominator by 8
8 = 1. So, the equivalent fraction is:
3 × 1
8 × 1 =
3
8
Step 4
Similarly, to write 7
2 as an equivalent fraction which has 8 as denominator, we need
to multiply both the numerator and denominator by 8
2 = 4. So, the equivalent fraction
is:
7 × 4
2 × 4 =
28
8
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
3
8 +
28
8 =
3 + 28
8 =
31
8
Step 6
ID : in-4-Fractions [22]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
In order to convert the fraction 31
8 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 31 and 8 is 1.
Step 8
Hence, the simplest/lowest form of 31
8 is
31
1
8
1
= 31
8
D) 4
5 +
7
10 =
3
2
Step 1
The fractions 4
5 and
7
10 are unlike fractions as their denominators are different.
We will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 10 and 5. The LCM is 10.
Step 3
To write 4
5 as an equivalent fraction which has 10 as denominator, we need to
multiply both the numerator and denominator by 10
5 = 2. So, the equivalent fraction
is:
4 × 2
5 × 2 =
8
10
Step 4
Similarly, to write 7
10 as an equivalent fraction which has 10 as denominator, we
need to multiply both the numerator and denominator by 10
10 = 1. So, the equivalent
fraction is:
7 × 1
10 × 1 =
7
10
ID : in-4-Fractions [23]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
8
10 +
7
10 =
8 + 7
10 =
15
10
Step 6
In order to convert the fraction 15
10 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 15 and 10 is 5.
Step 8
Hence, the simplest/lowest form of 15
10 is
15
5
10
5
= 3
2
E) 1
5 +
8
7 =
47
35
Step 1
The fractions 1
5 and
8
7 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 7 and 5. The LCM is 35.
Step 3
To write 1
5 as an equivalent fraction which has 35 as denominator, we need to
multiply both the numerator and denominator by 35
5 = 7. So, the equivalent fraction
is:
1 × 7
5 × 7 =
7
35
Step 4
Similarly, to write 8
7 as an equivalent fraction which has 35 as denominator, we need
ID : in-4-Fractions [24]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
to multiply both the numerator and denominator by 35
7 = 5. So, the equivalent
fraction is:
8 × 5
7 × 5 =
40
35
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
7
35 +
40
35 =
7 + 40
35 =
47
35
Step 6
In order to convert the fraction 47
35 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 47 and 35 is 1.
Step 8
Hence, the simplest/lowest form of 47
35 is
47
1
35
1
= 47
35
F) 5
3 +
6
2 =
14
3
Step 1
The fractions 5
3 and
6
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 2 and 3. The LCM is 6.
Step 3
To write 5
3 as an equivalent fraction which has 6 as denominator, we need to
multiply both the numerator and denominator by 6
3 = 2. So, the equivalent fraction is:
ID : in-4-Fractions [25]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
5 × 2
3 × 2 =
10
6
Step 4
Similarly, to write 6
2 as an equivalent fraction which has 6 as denominator, we need
to multiply both the numerator and denominator by 6
2 = 3. So, the equivalent fraction
is:
6 × 3
2 × 3 =
18
6
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
10
6 +
18
6 =
10 + 18
6 =
28
6
Step 6
In order to convert the fraction 28
6 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 28 and 6 is 2.
Step 8
Hence, the simplest/lowest form of 28
6 is
28
2
6
2
= 14
3
(14) improper
A fraction in which the denominator is smaller than the numerator is called an improper fraction.
ID : in-4-Fractions [26]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
(15) smaller
Step 1
Like fractions are those who have the same denominator. For such fractions the value of theoverall fraction depends directly on the value of their numerator.
Step 2
Therefore, in like fractions, smaller the numerator, smaller is the fraction.
ID : in-4-Fractions [27]
Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
![Mixed Fractions - Addition and Subtraction Class 6...Thus, the simplified value of the given fractions is 14 7 8. ID : in-6-Mixed-Fractions-Addition-and-Subtraction [9] (C) 2016 Edugain](https://img.pdfslide.us/doc/110x75/5f59799aafa4520ae1630d35/mixed-fractions-addition-and-subtraction-class-6-thus-the-simplified-value.jpg)
